A note on the Zenga index with respect to different results depending on grouping or not grouping the data

The Zenga index of inequality is a new proposal of measuring this phenomenon. The properties and empirical applications of Zenga index (and the underlying Zenga curve) have been recently widely investigated. Its advantages (and differences, as compared to other existing measures) have been pointed out. However, one of the possible problems associated with the use of the Zenga index has not yet been appropriately addressed.Namely, the Zenga index assumes different values depending on whether it is applied to grouped or ungrouped data. As it may seem that due to contemporary computers power it is not necessary to group data, the problem still exists as a conceptual one. Moreover, in some situations – such as applying equivalence scales – avoiding grouping of the data is not possible even in principle. The problem is stated, illustrated by simple numerical examples and briefly discussed in this paper.